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y=arctg^35x+lntgx
Derivada de la función/ x+lnt/ lntgx/ arctg/ y=arctg^35x+lntgx

Derivada de y=arctg^35x+lntgx

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    3                   
atan (5*x) + log(tan(x))
log⁡(tan⁡(x))+atan⁡3(5x)\log{\left(\tan{\left(x \right)} \right)} + \operatorname{atan}^{3}{\left(5 x \right)} 
atan(5*x)^3 + log(tan(x))
Gráfica
02468-8-6-4-2-1010-200200
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Trazar el gráfico f'(x)
Primera derivada [src] 
       2             2     
1 + tan (x)   15*atan (5*x)
----------- + -------------
   tan(x)               2  
                1 + 25*x
tan⁡2(x)+1tan⁡(x)+15atan⁡2(5x)25x2+1\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \frac{15 \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1}
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Segunda derivada [src] 
                             2                                   
                /       2   \                              2     
         2      \1 + tan (x)/    150*atan(5*x)   750*x*atan (5*x)
2 + 2*tan (x) - -------------- + ------------- - ----------------
                      2                      2                2  
                   tan (x)        /        2\      /        2\   
                                  \1 + 25*x /      \1 + 25*x /
−750xatan⁡2(5x)(25x2+1)2−(tan⁡2(x)+1)2tan⁡2(x)+2tan⁡2(x)+2+150atan⁡(5x)(25x2+1)2- \frac{750 x \operatorname{atan}^{2}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 2 + \frac{150 \operatorname{atan}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}}
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Tercera derivada [src] 
  /                            3                                   2                                                                   \
  |               /       2   \            2          /       2   \                                                        2     2     |
  |    375        \1 + tan (x)/    375*atan (5*x)   2*\1 + tan (x)/      /       2   \          11250*x*atan(5*x)   37500*x *atan (5*x)|
2*|------------ + -------------- - -------------- - ---------------- + 2*\1 + tan (x)/*tan(x) - ----------------- + -------------------|
  |           3         3                      2         tan(x)                                               3                    3   |
  |/        2\       tan (x)        /        2\                                                    /        2\          /        2\    |
  \\1 + 25*x /                      \1 + 25*x /                                                    \1 + 25*x /          \1 + 25*x /    /
2(37500x2atan⁡2(5x)(25x2+1)3−11250xatan⁡(5x)(25x2+1)3+(tan⁡2(x)+1)3tan⁡3(x)−2(tan⁡2(x)+1)2tan⁡(x)+2(tan⁡2(x)+1)tan⁡(x)−375atan⁡2(5x)(25x2+1)2+375(25x2+1)3)2 \left(\frac{37500 x^{2} \operatorname{atan}^{2}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{3}} - \frac{11250 x \operatorname{atan}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{3}} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{375 \operatorname{atan}^{2}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{375}{\left(25 x^{2} + 1\right)^{3}}\right)
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Gráfico
Derivada de y=arctg^35x+lntgx
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